Some aspects of the invention involve the advantageous use of technologies known in the art. In the following description some of these basic technologies will be introduced, for example, CFD, Gradient based methods, Evolutionary Algorithms (EA), and Artificial 25 Neuronal Networks (ANN).
Computational Fluid Dynamics (CFD) has become an integral part of aero/hydro-dynamic design processes, as, for example, the aircraft design process. It involves the use of computational methods to solve systems of nonlinear partial differential equations in order to predict how fluids will flow, and what will be their quantitative effects on the solids they are in contact with. Thereby, CFD complements experimental and theoretical fluid dynamics by allowing the efficient simulation of physical fluid systems. Another advantage CFD provides is the ability to model physical fluid phenomena that are difficult to measure in actual experiments. However, CFD simulations are computationally very expensive. What makes the problem more difficult is that EAs need a relatively large number of evaluations in order to achieve a near optimal aerodynamic design. To solve this dilemma, Artificial Neural Networks (ANN) can be used to approximate CFD computations.
ANNs are an important tool in soft computing that can advantageously be applied to solve a plurality of problems. The original purpose of an ANN is to simulate a biological neural system (e.g. a brain). To date, several neural network models have been developed, which can be applied to function approximation, classification, control tasks, and the like. An important issue that is closely related to ANNs is learning. Thereby, learning theory in ANNs has large overlap with that in Machine Learning (ML), Bayesian Theory and statistics.
In the following some background on optimization algorithms will be provided. The most well known ones are gradient-based methods (GMs), which probe the optimum by calculating local gradient information. These methods are efficient and the optimum obtained from these methods will be a global one, if the objective and constraints are differentiable and convex. Consequently, this approach has been widely used for many design problems including wing design, nozzle design, supersonic wing-body design, and more complex aircraft configurations. The quality landscape for an aerodynamic design problem, however, is usually multimodal. For GMs to find a global optimum, the optimization process has to be started repeatedly from a number of initial points and then checked for consistency of the obtained optima. In this sense, GMs are neither efficient nor robust for design optimization. Furthermore, for design optimization problems, the gradient information needed by GMs must be numerically estimated. This process can be computationally expensive and in general it is not very robust against noise.
By contrast, soft computing techniques such as Evolutionary Algorithms (EAs) form a new kind of iterative pseudostochastic optimization techniques that try to emulate mechanisms of natural evolution, where a biological population evolves over generations to adapt to its environment by means of selection, recombination and mutation. Such a population consists of a number of individuals composed of chromosomes, which are in turn composed of genes. These genes encode the parameters that need to be optimized for a given problem. If an EA is used for structure optimization, the parameters that describe said structure are encoded in said chromosomes. To eliminate unfavorable modifications and to proceed with modifications that increase the overall quality of the underlying population, a selection operation is used. Since techniques from computational intelligence like Evolutionary Algorithms (EAs) that employ objective function information (fitness values) instead of derivatives or other auxiliary knowledge—are known to be very robust, they have been enjoying an increasing popularity in the field of numerical optimization for practical engineering applications in recent years. EAs have been applied to aeronautical problems in several ways, including parametric and conceptual design of an aircraft, preliminary design of turbines, topological design of non-planar airfoils and aerodynamic optimization based on CFD.
Originally, there were three main streams of evolutionary computation—namely Genetic Algorithms (GA), Evolution Strategies (ES) and Evolutionary Programming (EP). More recently, Genetic Programming (GP) has been developed and has matured into the fourth major direction. When EAs are applied to optimization problems, individuals, genes and fitness values usually correspond to a design candidate, a number of design variables and an objective function value, respectively. One of the key features of EAs is that these algorithms search the design space population based, instead of moving from a single point like GMs do. Moreover, due to their stochastic component and the recombination of individuals the global optimum can be found, for most EAs theoretically even with probability one. Other advantages such as robustness, efficiency, suitability to parallel computing and simplicity make them particular useful candidates for a combination with CFD methods. The number of parameters (design variables) and the way in which the parameters describe the structure or surface, e.g., B-splines, Polygons, or alternative codings, are usually called the representation or the encoding of the design in evolutionary algorithms.
Experimental design optimization techniques using evolutionary algorithms (EAs) in particular evolution strategies, for example, as described in “Evolutionstratgie '94” (Frommann-Holzboog Verlag, 1994, incorporated herein by reference in its entirety) by I. Rechenberg and “Experimentelle Optimierung einer Zweiphasenduse-Teil (AEG Forschungsinstitut Berlin, Bericht 35-11.034/68, 1968, incorporated herein by reference in its entirety) by H.-P. Schwefel was one of the first application domains of this type of optimization methods. The necessary changes of the experimental design were carried out manually by adjusting devices that changed the design subject to said optimization. An example for this technique is the optimization of a pipe for re-directing the flow of a fluid or gas 90 degrees, in which screws were attached to the flexible material of the pipe. In this case, the employed evolution strategy was restricted to a (1+1)-population, so that the manual adjustment process remained feasible.
In “A Surrogate Approach to the Experimental Optimization of Multi-Element Airfoils” (Multi-Disciplinary Optimization Branch, NASA Langley Research Center March, 1996, Report RTR 505-59-53-08, incorporated herein by reference in its entirety) by J. C. Otto, D. Landman and A. T. Patera, the process described above is applied to the optimization of a multi-element airfoil, in which actuators are used to position the flap relative to the main element (2D change). Again, the measurement process is performed autonomously, the results are transmitted to the optimization algorithm, which uses a steepest ascent method and determines the best set-up of the relative wing positions for the next test.
In the article “Evolution Strategies for Computational and Experimental Fluid Dynamics Applications” (L. Spector, et al. (editors): Proceedings of the Genetic and Evolutionary Computation Conference (GECCO-2001), Morgan Kaufmann Publishers, San Francisco, Calif., 2001, incorporated herein by reference in its entirety) by F. Sbalzarini, S. D. Mueller, P. Koumoutsakos and G.-H. Cottet, an optimization of trailing vortices distraction using evolution strategies is disclosed. Thereby, Sbalzarini et al. study an implementation of two- and multi-membered evolution strategies to optimization problems for CFD applications in an experimental and computational environment, respectively.